Abstract
It has been shown by van den Berg and Steif [5] that the sub-critical Ising model on $\mathbb{Z} ^{d}$ is a finitary factor of a finite-valued i.i.d. process. We strengthen this by showing that the factor map can be made to have finite expected coding volume (in fact, stretched-exponential tails), answering a question of van den Berg and Steif. The result holds at any temperature above the critical temperature. An analogous result holds for Markov random fields satisfying a high-noise assumption and for proper colorings with a large number of colors.
Citation
Yinon Spinka. "Finitary coding for the sub-critical Ising model with finite expected coding volume." Electron. J. Probab. 25 1 - 27, 2020. https://doi.org/10.1214/20-EJP420
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